solve the following mathematical problems:

solve: $\frac{x}{2} + \frac{6}{y} = 9, \frac{x}{3} + \frac{2}{y} = 4$

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

$\frac{x}{2} + \frac{6}{y} = 9 \Rightarrow \frac{x y + 12}{2 y} = 9 x y + 12 = 18 y . . . . . . . . . . . (i) \frac{x}{3} + \frac{2}{y} = 4 \Rightarrow \frac{x y + 6}{3 y} = 4 x y + 6 = 12 y . . . . . . . . . . . (i i) N o w, [(i) - (i i)] w e h a v e (x y + 12 = 18) - (x y + 6 = 12 y) = (6 = 6 y) = (y = 1) p u t t i n g t h e v a l u e o f' y' i n (i i), w e h a v e (x \times 1) + 6 = 12 \times 1 \Rightarrow x = 12 - 6 x = 6 (x, y) = (6, 1)$